You will need special spearfishing fins, or freediving fins, whenever you are out spearfishing. (We don't call them flippers!) Spearfishing fins are longer, more flexible and of a simpler design than scuba diving fins as they are designed to get the spearfisher to greater depths while conserving energy and oxygen.
If you are just starting out in spear fishing, plastic fins are fine and will provide plenty of use and enjoyment. However if you are looking to take the next step in your spearfishing, it's beneficial for you to invest in carbon spearfishing fins as they will take you deeper more efficiently and, being higher in quality, will last you for many years.